Three leading Republican critics of United Nations Ambassador Susan E. Rice said that meeting with her Tuesday left them only more troubled about her potential nomination to be secretary of State.

Two of those Republicans, Sens. Lindsey Graham of South Carolina and Kelly Ayotte of New Hampshire, confirmed that they would, for the time being, at least, block her confirmation should the president decide to appoint her to succeed Hillary Rodham Clinton. Clinton has long made clear she intends to leave Foggy Bottom early next year.

Emerging from an hourlong meeting on Capitol Hill on Tuesday morning with Rice and Michael J. Morell, acting CIA director, Graham, Ayotte and Sen. John McCain, R-Ariz., pronounced themselves “more disturbed” than before their meeting about Rice’s qualifications for the top job in the State Department.

Their primary concern involves the Obama administration’s response to the September attack on a U.S. diplomatic facility in Benghazi, Libya, and Rice’s role in it. They said they also still have questions about how the intelligence community communicated information about the attack.

The three senators, as well as other GOP critics, have zeroed in on Rice’s statements on several Sunday morning news programs five days after the attack, when she claimed that the assault appeared to have been a spontaneous response to an anti-Muslim video.

There was “compelling evidence at the time that that was simply not the case,” McCain said Tuesday morning.

Intelligence officials now say that the assault was a coordinated effort by a fundamentalist Islamic militia, but they also have maintained that Rice was only repeating the unclassified talking points they provided officials at the time. President Barack Obama has fiercely defended Rice, a longtime foreign policy adviser, and said the GOP criticism has been an unwarranted, politically driven attempt to tarnish her reputation.

“The focus on a Sunday show appearance is entirely misplaced, and it represents less interest, I think, in what happened in Benghazi than in political dynamics in Washington,” White House spokesman Jay Carney said Tuesday.

In a statement released after the meeting, Rice acknowledged that the talking points on which she based her televised remarks “were incorrect in a key respect: There was no protest or demonstration in Benghazi.”

“While, we certainly wish that we had had perfect information just days after the terrorist attack, as is often the case, the intelligence assessment has evolved,” she said. She also thanked the senators for “the opportunity to discuss these issues directly and constructively with them.”

Senate Majority Leader Harry Reid, D-Nev., called the Republican attack on Rice “outrageous and utterly unmoored from facts and reality” in a statement released late Tuesday.

He added, “There should be no place for such blatant partisanship in oversight of our nation’s intelligence community. “

Rice’s meeting with the three senators prompted Sen. James M. Inhofe to walk back statements he made Monday indicating his opposition to a Rice nomination had softened.

“Yesterday, it seemed possible that Susan Rice had been unwittingly used by the Obama administration to misrepresent to the American people what really happened in Benghazi,” Inhofe said in a written statement released Tuesday evening. “After her meeting today on Capitol Hill with some of my colleagues, it is now clear that she willingly [misled] the American public five different times in the days after the attack.”

He also said that “there are more reasons to oppose a potential Rice nomination beyond the Benghazi issue,” citing her tenure at the United Nations and the United States’ inability to convince Russia and China to join them on U.N. initiatives on Iran and Syria.

On Monday, Inhofe told reporters he would not necessarily oppose Rice should Obama tap her as secretary of State. If Rice was simply repeating information she had been given by the administration or intelligence officials, “then she was thrown under the bus, and yeah, I’d feel different about it, if that’s the case,” he said.

McCain said the meeting with Rice on Tuesday raised questions about whether she “was prepared or informed sufficiently in order to give the American people a correct depiction of the events that took place.”

Graham added that “with a little bit of inquiry and curiosity, I think it would have been pretty clear” that the attack, which killed U.S. Ambassador J. Christopher Stevens and three other Americans, was part of a coordinated terrorist attack.

The group, along with some other Republicans, say this suggests a cover-up by the Obama administration, which they contend did not want to acknowledge it had failed to repel a terrorist attack.

“The storyline that the best current information was that this was a spontaneous event, spurred by a video, was an unbelievable stretch,” Graham told reporters later in the day Tuesday. “And the difference between spontaneous and pre-planned was significant. The difference between a mob and an organized militia is significant. And the motivation — we’re mad about a video versus we’re mad about America being in the Mideast — is significant.”

He also suggested that there were political reasons that the intelligence community dropped a reference to possible connections the attackers had with terrorist group al-Qaida in the unclassified talking points on which Rice based her public comments.

“We’ve had two reasons given thus far,” said Graham. “One is that we didn’t want to tip al-Qaida off. Please. Please. I think they know we’re onto them. No. 2, that it was a tenuous connection. . . . The question is, is there is a third reason?”

Rice rebutted the Republicans’ charges in her statement, saying she and Morell stressed in the meeting “that neither I nor anyone else in the administration intended to mislead the American people at any stage in this process.”

Rice did manage to satisfy one senator who has often been allied with McCain and Graham on matters relating to Libya.

Sen. Joseph I. Lieberman, I-Conn., said that his meeting with Rice was productive and that she has answered all of his questions.

“To say somehow or other that she misled the American people using the very notes that were asked for by the House Republicans and to accuse her of anything other than doing her homework, I think, is very, very unfair,” said a visibly agitated Levin. The language used in those talking points was “not her decision; that was the intelligence community’s decision.”

Levin said he had discussed the matter with former CIA Director David H. Petraeus and confirmed that Petraeus had signed off on the language.

“Take it up with the people who wrote the assessment. That’s fair game,” the normally even-keeled Democrat said. “But, my God, to tear into her!”

In addition to their issues with Rice, Graham and Ayotte said they want more information from the administration on the Benghazi attack before they would be willing to consider her nomination, and they plan to hold up her nomination in the meantime.

“We’ve got to answer questions before we can make good judgments,” said Graham. “No. 1, where is the FBI interview of the survivors? Why don’t we have that? Where are the cables from Sept. 11 coming back from the headquarters about what’s going on here? I mean, this is basic stuff.”

Ayotte said Tuesday she also requested “to review all the State Department cables” with the embassy in Tripoli. “I’ve been denied that because I’ve been told I’m not on the Homeland Security or Foreign Relations Committee, which is the most absurd thing I’ve heard,” she said.

“There are still so many questions that need to be answered related to the attacks on the consulate in Benghazi, including, I think there will still be follow-ups to Ambassador Rice,” Ayotte said.

Carney flatly rejected that. “I would simply say that there are no unanswered questions about Ambassador Rice’s appearances on Sunday shows,” he told reporters Tuesday. “The talking points that she used for those appearances that were provided by the intelligence community, those questions have been answered.”